The maximum number of components into which a vector can be resolved in its own plane is

Options

A. 2
B. 3
C. 4
D. more than 4

Answer

To determine the maximum number of components into which a vector can be resolved in its own plane, we can follow these steps:

### Step 1: Understand the concept of vector resolution
A vector can be resolved into components along specified directions. In a two-dimensional plane, the most common resolution is into two perpendicular components, typically along the x-axis and y-axis.

### Step 2: Visualize the vector in a plane
Consider a vector **A** in the xy-plane. This vector can be represented as having a certain magnitude and direction. Let's denote the angle it makes with the x-axis as θ.

### Step 3: Resolve the vector into components
When we resolve vector **A** into components:
- The component along the x-axis (horizontal) is given by \( A_x = A \cos(\theta) \).
- The component along the y-axis (vertical) is given by \( A_y = A \sin(\theta) \).

### Step 4: Identify the maximum number of components
In a two-dimensional plane, a vector can be resolved into two components, which are perpendicular to each other. These two components are sufficient to represent the vector completely in that plane.

### Conclusion
Therefore, the maximum number of components into which a vector can be resolved in its own plane is **2**.

### Final Answer
The maximum number of components into which a vector can be resolved in its own plane is **2**.

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